Bull. Austral. Math. Soc. 72(1) pp.129--138, 2005.
On the monotonicity properties of additive representation functions
Yong-Gao Chen |
András Sárközy |
Vera T. Sós |
Min Tang |
Research supported by the NSF of China Grant 10471064, the SF of AnHui Province Grant 01046103 and the Hungarian National Foundation for Scientific Research Grant T043623, T042750, T038210, T046378.
Abstract
If A is a
set of positive integers, let R1(n) be the number of
solutions of a + a' =
n, a, a' 
A, and let
R2(n) and
R3(n) denote the
number of solutions with the additional restrictions a < a', and a 
a' respectively.
The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and
compared.
A, and let
R2(n) and
R3(n) denote the
number of solutions with the additional restrictions a < a', and a a' respectively.
The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and
compared.Click to download PDF of this article (free access until July 2006)
or get the no-frills version
[an error occurred while processing this directive]| (Metadata: XML, RSS, BibTeX) | MathSciNet: MR2162298 | Z'blatt-MATH: 02212190 |
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ISSN 0004-9727